<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="scmpds_4.html#V2">parahalting</a> <a href="scmpds_5.html#V3" target="_self">No-StopCode</a> <a href="scmpds_4.html#NM1">Program-block</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="scmpds_4.html#V2">parahalting</a> <a href="scmpds_4.html#V3">shiftable</a> <a href="scmpds_4.html#NM1">Program-block</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="ami_2.html#K2">SCM-Data-Loc</a> ;<br/>
<b>assume </b><a NAME="E1:60"/><i><font color="Green">E40</font></i>: 
(  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> )
 ;<br/>

<b>then </b><i><font color="Green">E41</font></i>: <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T14" target="_self">Th14</a></i>
;<br/>
<a NAME="E3:60"/><i><font color="Green">E42</font></i>: 
 <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_4.html#T57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E4:60"/><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>;<br/>
<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:60_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 ;<br/><a NAME="E2:60_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/><a NAME="E3:60_2"/><b>then </b><i><font color="Green">E46</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_2_1"/>
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  )
 </span><b>by </b><i><a class="txt" href="scmpds_5.html#E3:60_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scmpds_4.html#T28">SCMPDS_4:28</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_2_1_1"><b>suppose </b></a><a NAME="E1:60_2_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:60_2_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/><b>hence </b><a NAME="E3:60_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E3:60_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmpds_5.html#E1:60_2_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmpds_4.html#T22">SCMPDS_4:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_2_1_2"><b>suppose </b></a><a NAME="E1:60_2_1_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E2:60_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_3.html#T6">SCMPDS_3:6</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:60"/><i><font color="Green">E45</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:60"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E8:60"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E9:60"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E10:60"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="xboole_0.html#K3">/\</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E8:60"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E11:60"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E12:60"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E13:60"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E5:60"><i><font color="Green">E44</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E14:60"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E4:60"><i><font color="Green">E43</font></i></a>, <a class="ref" href="lattice2.html#T8">LATTICE2:8</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<a NAME="E15:60"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmpds_5.html#E2:60"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmpds_5.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E16:60"/><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E6:60"><i><font color="Green">E45</font></i></a>, <a class="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/>
<a NAME="E17:60"/>
 <a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_5.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E18:60"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E19:60"/><i><font color="Green">E51</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_5.html#T30" target="_self">Th30</a></i>;<br/>

<b>thus </b><a NAME="E20:60"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="txt" href="scmpds_5.html#E14:60"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmpds_5.html#E15:60"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmpds_4.html#T24">SCMPDS_4:24</a></i>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> as   <a href="nat_1.html#NM1">Nat</a> ;<br/>
 <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> 

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmpds_4.html#K3">';'</a> <a href="scmpds_3.html#K5">SCMPDS-Stop</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T46">SCMPDS_4:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6">Shift</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

;<br/>
<a NAME="E23:60"/><b>then </b>
 <a href="scmpds_3.html#K6">Shift</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmpds_4.html#K8">stop</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E24:60"/><b>then </b>
 <a href="scmpds_3.html#K6">Shift</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E3:60"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E25:60"/><i><font color="Green">E53</font></i>: 
 <a href="scmpds_3.html#K6">Shift</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>

<div><i><font color="Green">E54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>17</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:60_4"/>
<span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><a NAME="E2:60_4"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>assume </b><a NAME="E3:60_4"/><i><font color="Green">E56</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> = 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_5.html#E6:60"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmpds_5.html#E19:60"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmpds_5.html#E20:60"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmpds_5.html#E25:60"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_4.html#T84">SCMPDS_4:84</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="txt" href="scmpds_5.html#E3:60_4"><i><font color="Green">E56</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><b>hence </b><a NAME="E5:60_4"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_5.html#E16:60"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmpds_5.html#E2:60_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E27:60"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E6:60"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmpds_5.html#E19:60"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmpds_5.html#E20:60"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmpds_5.html#E25:60"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_4.html#T84">SCMPDS_4:84</a></i>;<br/>
<a NAME="E28:60"/><b>then </b>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p0">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/>
<a NAME="E29:60"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E16:60"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>17</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:60_5"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_5_1"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font> or  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_5_1_1"><b>suppose </b></a><a NAME="E1:60_5_1_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_5_1_1"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmpds_5.html#E18:60"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmpds_5.html#T32" target="_self">Th32</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_5_1_2"><b>suppose </b></a><a NAME="E1:60_5_1_2"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>18</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:60_5_1_2"/><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><b>thus </b><a NAME="E4:60_5_1_2"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmpds_5.html#E26:60"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmpds_5.html#E1:60_5"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmpds_5.html#E3:60_5_1_2"><i><font color="Green">E57</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E31:60"/><b>then </b><i><font color="Green">E56</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a>  holds <br/><font color="Maroon">c<sub>16</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 
;<br/>
<a NAME="E32:60"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_4.html#T63">SCMPDS_4:63</a></i>;<br/>
<a NAME="E33:60"/><b>then </b><i><font color="Green">E57</font></i>: 
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E29:60"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmpds_5.html#E31:60"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>
<a NAME="E34:60"/>
 <a href="scmpds_4.html#K2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_5.html#E1:60"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E35:60"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T63">SCMPDS_4:63</a></i>;<br/>
<b>hence </b><a NAME="E36:60"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K8">stop</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_5.html#E33:60"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmfsa6b.html#T16">SCMFSA6B:16</a></i>;<br/>


</div>
